Uncertainty in machine learning is usually categorized by two different terms. Epistemic uncertainty arises from the uncertainty about the trained model, that is about \(\theta \)  in the notation of (REF ). In a Bayesian approach, as in this work, this uncertainty is described by the posterior \(\pi (\theta |\mathcal {D})\) , which is the distribution of \(\theta \)  conditional on the data \(\mathcal {D}\)  [1]}, [2]}, [3]}. This type of uncertainty vanishes as the number of observations tends to infinity, as follows for instance from the Bernstein-von Mises theorem. Aleatoric uncertainty, on the other hand, describes an uncertainty that is inherent to the data and cannot be diminished even with an infinite training set. In the context of regression this would correspond to a noise such as \(\varepsilon _y\)  in (REF ) and might be measured, for instance, by \(\sigma _y\) .
